Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C24 |
| direct product | C2×C22⋊#11758187 |
| Sylow | C61 ⋊ C2×C22⋊C16 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C2×#6923 |
| commutator | C2×C61 | C22×C16 |
| Frattini | C2×C4 | C22×#6923 |
| Fitting | C23×C4×C61 | C4 |
| socle | C23×C61 | C2×C8 |
| hypercenter | C23×C4 | #6923 |
| hypocenter | C61 | C2×C22⋊C16 |
| LCS | G ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C22×C4 ◁ C23×C4 | |
272 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 122 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
560 conjugacy classes — view the full character table.
| maximal subgroup of | #30594327, #30594328, #30594336, … |
| maximal normal subgroup of | #30594327, #30594328, #30594336, … |
| maximal quotient of | C2×#21460739, C2×#21460755, #30603924, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 20734);